Cohen reached out to Vladimir Putin's chief spokesman in an effort to advance the building's construction after the project began to stall, according to the Post, who cited several people familiar with document subpoenas and witness interviews. Cohen said he did not recall receiving a reply from the spokesman, the Post said.

Cohen attorney Stephen Ryan disputed the report, telling the Post in a statement: "Unsourced innuendo like this succeeds only because the leakers know the Special Counsel will not respond to set the record straight."

Cohen's lawyer did not immediately respond to CNBC's request for comment.

In another instance, a Ukrainian lawmaker reportedly sent Cohen a peace proposal for Ukraine that was favorable to Russia. The proposal was delivered one week after Trump took office, the Post said, citing sources.

The White House did not immediately respond to CNBC's request for comment.

The Post's report is not the first time Trump Tower Moscow has been raised as a possible area of interest for the Mueller investigation.